(1) Field of the Invention
The invention generally relates to Transform Picture Coding. In broad outline this is a method of converting an array of N.times.N multibit input data words into an array of N.times.N multibit output data words by means of a two-dimensional linear transform. More particularly, an array of pixels of a television picture is converted into an array of so-called coefficients, or conversely. In the former case the term forward linear transform is generally used and in the latter case the term inverse linear transform is generally used.
Transform Picture Coding is a subject which is currently in the limelight because it appears to be the means to realise a significant bit rate reduction in the transmission of television pictures in a digital form and having a predetermined quality.
It can be used in television broadcasting systems in which the atmosphere is the transmission medium, in video conference systems in which a transmission cable is usually present as a transmission medium and also in video recorders in which a magnetic tape is the transmission medium.
(2) Description of the Prior Art
It is generally known that for performing a forward two-dimensional linear transform the television picture is split up into sub-pictures each of N.times.N pixels and each sub-picture is considered as a sum of N.times.N mutually orthogonal basic pictures B.sub.i,k each also of N.times.N pixels and each with its own weighting factor y.sub.i,k. Here it applies that i, k=0, 1, 2, . . ., N-1. These weighting factors are commonly referred to as the coefficients of the linear transform.
Due to the correlation between the pixels of a sub-picture the information is concentrated in a limited number of basic pictures. Only the associated weighting factors are important and the other weighting factors can be ignored.
In order to determine these weighting factors, a sub-picture is considered as an array X of N.times.N pixels X.sub.i,k. Furthermore an orthogonal N.times.N transform matrix A is defined which relates to the selected collection of basis pictures B.sub.i,k. More particularly it holds that: EQU B.sub.i,k =A.sub.i A.sub.k.sup.T ( 1)
In this expression A.sub.i represents an N.times.N matrix in which each column is equal to the i-th column of the transform matrix A and A.sub.k.sup.T represents an N.times.N matrix each row of which is equal to the k-th row of the matrix A.
If the weighting factors Y.sub.i,k are assumed to form the elements of N.times.N coefficient array Y, the said coefficients then follow from the matrix multiplication EQU Y=A.sup.T .times.A (2)
In this expression A.sup.T represents the transposed matrix of A.
For more information relating to the above reference is made to Reference 1.
For the calculation of the coefficients in accordance with expression (2) both the transform matrix A and its transposed version should be available. Expression (2) is, however, equivalent to EQU Y.sup.T =(XA).sup.T A (3)
This matrix multiplication only requires the matrix A. More particularly the product array P=XA can be calculated first, subsequently P can be transposed and finally Y.sup.T =P.sup.T A can be calculated.
In order to recover the original array X of pixels from the array Y of coefficients thus obtained, this array Y is subjected to an inverse two-dimensional transform. This is defined as follows. EQU X=AYA.sup.T ( 4)
This expression is in its turn equivalent to EQU X=A(AY.sup.T).sup.T ( 5)
Starting from the array Y.sup.T the product matrix P'=AY.sup.T can be calculated first. Subsequently P' can be transposed and finally the product X=AP'.sup.T can be determined.
The above-mentioned product matrices P=XA, Y.sup.T =P.sup.T A, P'=AY.sup.T and X=AP'.sup.T are each obtained from a series of so-called vector matrix multiplications. For example, for obtaining the product matrix P a row of X is multiplied by each column of A in order to obtain the corresponding row of P. Generally a vector matrix multiplication will hereinafter be referred to as a one-dimensional transform and a device for performing such a transform will be referred to as a one-dimensional transformer. More particularly the product arrays P and Y.sup.T are obtained by one-dimensional forward transformation of X and P.sup.T, respectively and the product arrays P' and X are obtained by one-dimensional inverse transformation of Y.sup.T and P'.sup.T, respectively.